One of the fundamental phenomena in optics is refraction, wherein naturally occurring materials obey Snell's law as a result of having positive refractive indices. However, in the 1960s, Veselago considered a notional material that had a negative refraction and proposed its use as a flat lens. Within the last several years, work on metamaterials and ‘perfect lenses’ revived Veselago's ideas and trigged intense discussions. Meanwhile, negative refraction was also investigated in photonic crystals (PhCs) by engineering their dispersion properties. Along these lines, experiments have demonstrated negative refraction and imaging based on negative refraction by two-dimensional PhC flat lenses. More recently, we demonstrated experimentally subwavelength imaging at microwave frequencies with a three-dimensional (3D) PhC flat lens that exhibited a full 3D negative refraction.
The belief that light carries momentum and therefore can exert force on electrically neutral objects by momentum transfer dates back to Kepler, Newton and Maxwell. However, the radiation force had not attracted much interest until the invention of lasers, which can generate light of extremely high intensity and thus exert a significant force on small neutral particles. This capability enables an unprecedented tool to trap and manipulate small particles ranging in size from the micrometer-scale down to molecules and atoms, as well as to drive specially designed particles as sensitive nano-probes. The techniques based on radiation force have found applications in a wide range of fields including biomedical science, atomic physics, quantum optics, isotope separation, and planetary physics. One of the most successful applications is the use of optical tweezers, which relies on a single-beam gradient-force trap. In biology, optical tweezers are widely used for their ability to nondestructively manipulate small particles ranging in size from tens of nanometers to tens of micrometers. In atomic physics, optical tweezers have found applications in cooling atoms to record low temperatures and trapping atoms at high densities. To implement the optical tweezers for achieving a stable trap, one requires a highly focused and strongly convergent laser beam, which is often realized through a microscope system and is limited by the working wavelength and numerical aperture (N.A.). To manipulate or “tweeze” particles in a large field of view, the system is required to be devoid of field curvature. However, high N.A. and small field curvature are often incompatible in a conventional optical system. In practice, optical tweezers are very expensive, custom-built instruments that require a working knowledge of microscopy, optics, and laser techniques. These requirements limit the application of optical tweezers.
In the Rayleigh scattering regime (λ>>r, where r is the radius of the particle.), the radiation force acting on a dielectric particle can be explained as the interaction between the polarized particle and the applied electric field. The radiation force produced by a focused beam has two components: scattering force and gradient force. Optical tweezers rely on the gradient force, which is proportional to the dipole moment of the particle and the gradient of power density. For a spherical particle in a dielectric liquid medium, the total dipole moment can be shown to take the form
      p    =          4      ⁢                          ⁢      π      ⁢                          ⁢              r        3            ⁢                        ɛ          b                ⁡                  (                                                    ɛ                a                            -                              ɛ                b                                                                    ɛ                a                            +                              2                ⁢                                  ɛ                  b                                                              )                    ⁢      E        ,where ∈a and ∈b are the dielectric constants of the particle and the medium, respectively, and E is the applied electric field. For simplicity, we approximate the beam focused by the flat lens as a Gaussian beam. In this case, the maximum gradient force is
            F      grad        ∝                  r        3            ⁢                        ɛ          b                    ⁢              (                                            ɛ              a                        -                          ɛ              b                                                          ɛ              a                        +                          2              ⁢                              ɛ                b                                                    )            ⁢              P                  W          0          3                      ,and the resulting gradient acceleration is
      a    ∝                            ɛ          b                    ⁢              (                                            ɛ              a                        -                          ɛ              b                                                          ɛ              a                        +                          2              ⁢                              ɛ                b                                                    )            ⁢              P                  W          0          3                      ,where P is the power and W0 is the diameter of the beam waist. Since the acceleration is inversely proportional to the cube of the beam width, squeezing the beam size is a very efficient way to increase the acceleration, and thus improve the particle trapping.